Table 1: Numerical results of Example 1.

Exact solutionLegendre waveletsAbsolute error

0.011.0000208580.000020858
0.10.99004983370.99004493750.0000048962
0.20.96078943920.96079628850.0000068493
0.30.91393118530.9139303816
0.40.85214378900.85213540210.0000083869
0.50.77880078310.77878791220.0000128709
0.60.69767632610.69762308120.0000532449
0.70.61262639420.61241948540.0002069088
0.80.52729242400.52669847610.0005939479
0.90.44485806620.44343811680.0014199494
10.36787944120.36480168920.0030777520